Need advice on how to ensure new blank hardrive is properly partioned

I have a Windows Vista desktop on which I will be installing Windows 7 Home Premium
I will be removing the installed 250GB hard drive and will be replacing it with a 250GB SSD
It isnít necessary for me to replace the hard drive but I want the experience of installing a new hard drive and doing a fresh Win7 install on the blank hard drive.

One of my main concerns right now is how to ensure the hard dive is properly partitioned as I have seen so many hard drives partitioned very differently from each other
--- Iím OK with everything being on drive C as that is what Iím used to

The System partition of 350MB is on the left
The Windows C partition of 457.690GB is in the center
The Recovery partition of 7.82GB is on the right: is 7.82GB a typical setup?
--- Is that setting it up on the right correct?

I have a Win7 HP install disc from TigerDirect
--- Is it reasonable to expect it to set up the System & Recovery Partitions or will I have to figure how to do them myself?
If I have to do them myself, how do I do that?

If installing Win7 clean on the new 250GB SSD just let it do its thing, equivalent to building a Custom computer. I normally don't find it necessary to do partitioning function ahead of the install, in fact I did a Win7 and a Win10TP yesterday on clean drives. If using a separate data drive I also prefer not having it connected until after Windows is up and running.

The difference with using OEM Factory Restore discs is the setup will create the partitions as they are needed.

Since I am not experienced at setting up hard drives, it’s good to know it will be set up properly on a blank hard drive. Most likely I would be following the default settings but I like to have some basic understanding on what’s going on and what can I do if a decision needs to be made beyond the default settings. and this is where your advice is very helpful for me.
On formatting the hard drive, does that mean I have to ensure it’s formatted as NTFS?
There have been times when I’ve read that initializing a hard drive is required:
--- When and how do I determine that?
The fact that there will not be a recovery partition makes sense to me as my install disc will be my recovery method if it’s ever needed
--- Once I have the install and Windows Updates completed, I’ll make a pristine system image with Macrium Reflect Free and follow up with monthly system images

As you are using an existing hard drive, it doesn't need formatting. Likewise doing an initial install on a new hard drive. The W7 disk does everything for you. The only time you will normally need to format a drive is when you fit a new drive as a secondary drive. This is done to allow Windows to recognise it. NTFS is the normal format for Windows.

...I have a Win7 HP install disc from TigerDirect
--- Is it reasonable to expect it to set up the System & Recovery Partitions or will I have to figure how to do them myself?
If I have to do them myself, how do I do that?

With only the SSD connected boot from your Win7 installation DVD, press "any key to boot from CD/DVD" to launch Windows setup. At some point you will be prompted for the location to install Windows and the (empty, unpartitioned) SSD should be pre-selected. You should only need to click "Next" and Setup will create the partitions and format them and install Windows.

Normally there will be a "System Reserved" partition as the first partition on the drive, and a second partition which will probably show as "Local Disk" in Computer after Windows Setup completes. You can change the disk lable from "Local Disk" to your preference later by adjusting the "Properties".

The "Recovery" partition in the screenshot in your #1 post applies only to an OEM installation (HP, ASUS, Acer, Lenovo, etc.) and is not applicable to a clean install using a standard Windows install disk. It is provided by the OEM to allow users to revert Windows to "factory defaults" status.